Moment of Inertia Basics
When objects rotate, Newton's Second Law takes a special form: angular acceleration = net torque ÷ moment of inertia . The moment of inertia (I) represents an object's rotational inertia - how much it resists changes in rotational motion.
Different shapes have specific formulas for calculating moment of inertia. For example, a thin rod rotating about its center has I = ML², while the same rod rotating about its end has I = ML². Notice how the value increases when rotation occurs farther from the center of mass!
Other common shapes include a plane (I = Ma² about center), a cylinder/disk (I = MR² about center), and a solid sphere (I = MR² about diameter). The formula always includes both the object's mass and the square of a distance measurement.
Think About It: Why does moment of inertia depend on both mass AND the distribution of that mass? The further mass is from the rotation axis, the harder it is to start or stop rotation!
